?In the following exercises, estimate the volume of the solid under the surface \(z\) =

Chapter 5, Problem 11

(choose chapter or problem)

In the following exercises, estimate the volume of the solid under the surface \(z\) = f(x, y) and above the rectangular region \(R\) by using a Riemann sum with \(m\) = \(n\) = \(2\) and the sample points to be the lower left corners of the subrectangles of the partition.

The solid lying under the surface \(z=\sqrt{4-y^{2}}\) and above the rectangular region \(R=[0,\ 2]\times[0,\ 2]\) is illustrated in the following graph. Evaluate the double integral \(\iint_{R} f(x, y) d A\), where \(f(x,\ y)=\sqrt{4-y^2}\), by finding the volume of the corresponding solid.

Text Transcription:

z = f(x, y)

R

m = n = 2

z=\sqrt{4-y^{2}}

R=[0,\ 2]\times[0,\ 2]

\iint_{R} f(x, y) d A

f(x,\ y)=\sqrt{4-y^2}